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What is the advantage of using Direct Web Remoting over a REST web services design?

I have an enterprise Java web application deployed in tomcat.
I am looking for ways to integrate a HTML & JS UI with the mid tier java code. So far, from looking around I have read that there are two ways to do this which fit my requirements :
1) DWR - Direct web remoting
2) Use REST web services.
I am not sure which approach to use.
Edit: What is the advantage of using DWR over a rest WS design?
Is there a better approach available? Some people asked me to have a look at GWT, but I am not sure if these are scalable.
Edit 2: I will most likely be using dojo for the UI development(Works well with REST/DWR??), and I want to keep the java code chages minimal. I understand that by using web services, I would have to write an additional WS client layer on top of the existing java code.
Also, the usual enterprise needs, performance, scalability, etc.

Ok so you're building a web client frontend to your java backend, there are a few ways to go about this:
You want to use java standards as much as possible, preferably living in the java EE world: JSF. You will need some knowledge of HTML, XML and perhaps even javascript (though limited). Personally I have had a pretty buggy experience with JSF+richfaces to the extent that I don't use it anymore.
You are very well acquainted with java desktop application development but don't know much about javascript: vaadin: it allows you to write plain java using desktop application terminology which will be compiled to javascript. Currently I am working on a big vaadin project and it is very nice to be working with pure java in eclipse, the downside is however that you are far removed from the actual frontend, so tweaking can be tricky. Additionally everything is stored in sessions (afaik) and scales poorly.
You are primarily a frontend person with unrivaled javascript skills: use a REST interface in java and a pure js/html/css frontend. Personally I think this is the cleanest design and I have designed a few of my own applications like this. The downside is that managing large javascript projects tends to be hard because...well...javascript sucks. The upside is that this will always be the fastest most lightweight option available to you.
Ideologically I would definitely suggest the last approach but this can be hard for large projects. If you have the hardware to throw at it, vaadin is a nice option. My JSF 2 experience was a bit disappointing due to the bugs in (necessary) third party libraries like richfaces.
PS: I have never heard of DWR but the last stable release seems 2 years old and all it seems to do is expose java code as javascript methods which can be better handled with a REST interface.

Open interface standards like REST and SOAP make it easy to build code to consume these services if you are using frameworks to build a REST Client and a SOAP client code respectively. But the point is that you need to have this client code to make calls to these services.
DWR on the other hand, generates this client code. Your java classes are ready to be called (like you would do in Java).

Confusion Over Google's GWT?

I have just been looking at the GWT and i am impressed by what i have seen but i do not really understand how it is used to when creating web applications.
For example, when im programming in PHP or JSP creating a simple app that lets users register, adds the detailes to a database and then allows them to login is pretty simple but i was wondering how GWT does this?
When doing this in GWT, would GWT widgets be used to construct a frontend(client) that accepts user input and then sends it to a server which is written using pure Java, the Java then does all of the data processing and database interfacing?
If my understanding is correct, is GWT just a way to write javascript frontends in an easier way?

Have you looked into the GWT Overview? I think this line explains it the best:
The GWT SDK contains the Java API
libraries, compiler, and development
server. It lets you to write
client-side applications in Java and
deploy them as JavaScript.
Basically, you write your code in Java, all the while using the GWT to create complex UI's, etc. When you "compile" it, it is highly optimized JavaScript that translates well to multiple browsers, including web platforms.
Whatever language you want to use server-side does not matter - ASP.NET, PHP, etc - it will all work with GWT because GWT is, ultimately, JavaScript.
Basically, Google is trying to make it simple to develop web applications in a familiar language, and doing all the underlying work for you. I'm sure there is someone else who can further expand on the capabilities and advantages of GWT, but I hope this helps!

Exactly. "In the end, it's just JavaScript", you can "Use the backend language of your choice"

Which Java technology should I use, if I want to build a website with thousands of users?

Sorry for asking this question, but I searched all Java-related questions, but I got more confused. I am still not clear what should I start with.
My main thing is building websites in Java, because someone told me that there are some machine learning or AI libraries available in Java which I can use in Java. So I decided to use that as it can reduce my work.
Now I don't know Java at all. Some people say the following are used to build websites, like:
Servlets alone can build a website
JSP alone can also build a website
Struts
Spring Framework with Hibernate
Seam
Java EE also for websites
I am confused. Where should I start from? Where does core Java fits in here?
I was thinking of perhaps learning Python as I know I have to learn Python only, not its variations.
So please guide me to one thing which can solve my basic purpose of using ready-made libraries of AI.
If I can do that with JSP then I will start with that.
But if I need to learn all of them, then it’s better if can start learning Python.
I have five months to finish the website.
I really don't know why there are many branches of Java for doing one thing.

To correct some misconceptions of yours:
servlets and JSP are Java EE
Seam and Struts can be used together with Hibernate as well
Spring MVC is a web framework. Spring as a dependency injection framework can be used together with any other framework.
there are many more options, like JSF, Tapestry, Click, Play, etc.
It depends on what will the site will be doing, but you can choose any.

Experience has shown that building complex HTML forms (especially validation) and Ajax functionality is hard to get right. You will most likely appreciate having a library to assist you with that. The same thing with database access.
Everything builds on servlets. Learn those in order to understand the libraries you will use.
I would suggest learning JavaServer Faces (JSF) with facelets. The easiest, while being powerful, is JSF 2 in Java EE 6. The easiest way to get started is to use NetBeans with GlassFish 3.

For static web pages, HTML alone is enough and if you want to make it more user-friendly and interactive, use JavaScript.
There are lot of frameworks you can use directly in JavaScript, like jQuery. Now if you want to make some more functionalities, like database interaction, then you will need either PHP, Java (JSP and Servlets) or .NET (there exist some more, but I’m aware of three only). Each of them have their library to interact with database.
Since you are interested in Java, go through Servlets, HTML, JavaScript, and JSP. Once this is done, you can look into JSF and EJB beans. So if you have knowledge of Java this will not take too much time, because the syntax is the same; the only difference is the concept.
So you will have a frontend (HTML, JS, and JSP) which will interact with the backend (Servlets and the database) which will be deployed in a Web container. To deploy, you can use an one of the available application servers, like Apache Tomcat, GlassFish, or WebSphere. To develop your application, you can use Eclipse as the IDE, which is one of the best IDEs I have used.
So decide your architecture and design, break it into components and start writing small applications first. Once you are experienced in small application, start writing an application where there are more things you have to care of, like load on database, availability, security, etc. For that, you can refer a very famous question on Stack Overflow, What technical details should a programmer of a web application consider before making the site public?.

The closest to core Java is servlets. No extra syntax, very minimal library, but no included functionality.

For building websites, the main thing is HTML and HTTP.
All technologies (including Enterprise Java or Server side Java) do the same—to understand an HTTP request and respond back with HTML. All that you mentioned do the same thing with a different level of sophistication.
Start with Wikipedia.org to know what technologies do what. If you are completely new to Java, go through the Sun tutorials, do sample programs, and get comfortable with Java packages, JVM and classes. (This might take a week or two).
To build websites using Java, you'll have to learn Java Servlets—everything else (JSP, Struts, JSF, and Spring(!)) are built on it. Get Head First books on Java and Servlets; they will be useful.

You can always build the page in Ruby or something that will give you a website very fast. For the AI stuff that analyzes the bought items for the recommendations, use something unrelated to the page that only takes the database to work with.
I would not mix the whole web page stuff with the AI computing. You can do the AI things that will take a long time and maybe should done on a different machine to have your webpage also responsive with C++ or Java in normal applications.
Choosing your front end technique because of later usage is a very dangerous thing. Using the whole Java EE concept and learning it from scratch will take you much longer than have a quick start with your page if you do it in Ruby or PHP.
You can then build the first version of the page and generate a user base. Start working on the AI stuff once you got some data with other technologies.
If your page has performance problems because your technology does not scale, you can always begin switching parts of the stuff out with a faster technology or maybe simply a bigger machine. Get your page running before you build it bulletproof for the thousand users you are expecting.

If you’re trying to build a website from scratch, with no prior knowledge, your best bet is to go with frameworks that provide a complete stack for web development.
If you aren't dead set on Java, you could probably start learning Ruby on Rails, which would be easier to start with (if so, go buy a Ruby on Rails tutorial which goes through all the necessary things for modern web development, from MVC to version control).
For Java, try:
Play Framework is very similar to Ruby on Rails. It will get you started very quickly, and hopefully (if you follow conventions) handle all of your peripheral needs.
Spring Roo is a very-fast-to-work-with framework, but it might get hard to maintain and extend later on.
These two are full web frameworks, that is, they handle database, MVC (presentation layer), configuration setting, etc... (I'll explain shortly). And could even ease your deployment process.
If you're going to go through any other route (using several frameworks together), you are probably not going to finish what you are doing in five months.
To understand why, and to clear some things you wrote in your question, you need to understand that modern web development (and enterprise development as a whole) is comprised of several different technologies:
Presentation: the term web frameworks has been more or less taken to mean frameworks that deal with this side of web development, i.e., how to create a web page (an HTML page). Most of the frameworks offer an MVC like approach (which you can read about elsewhere), and this is what most of the frameworks/technologies you gave sit in—JSP and Struts (which uses JSP) are examples of web frameworks. Servlets is a lower-level API that standardizes how to answer HTTP requests (which JSP and Struts sit on top of).
Persistence: being able to show a webpage doesn't mean squat these days if you can't save data to a database, and that is what the persistence frameworks do (they ease the way you can save data to the database). Hibernate is a persistence framework.
For Java there are also dependency injection (DI), which is what Spring DI is. It's tough to explain DI to people not familiar with the troubles of Java, so I won't try to explain it, but it's a very important part of modern Java development.
apart from these core technologies, there are also many items that you'll need to learn to actually deploy the application (unless your using services like Heroku or Google App Engine, which should simplify things), and troubleshoot it later (understanding how concurrency and HTTP works).
To address the other technologies you brought up:
I've never really touched Seam, so I'm not sure, but it looks like a collection of other frameworks (mainly EJB 3, which itself is a collection of APIs, and JSF).
Spring denotes a popular open source group (the SpringSource group) that provides various technologies, but most likely when you hear about it they refer to two things Spring's dependency injection (DI) and Spring's MVC (which is a web framework).
Java EE is merely a collection of high level APIs which other technologies implement (Hibernate implements JPA which is part of Java EE for instance).

Which programming skills do I need to have to write an application in Google Application Engine?

I want to use java platform and I don't know what else I need to know about to write apps in google app engine?

According to this introduction, you'll need at least the following (assuming you already know Java):
the general concepts of standard Java web development (e.g. servlets, war files, JSP, session, request/response, etc)
the JDO persistence framework (Java Data Objects)
using the Eclipse IDE and the GAE plugin
However, rather than asking about skills, you'll be better off to work through the tutorial, and identify areas that you don't understand.

You will need to learn how to write Java web applications as the Google engine provides a nearly complete servlet API implementation.
First you need to learn how to use Java. The Sun Java Tutorial is a good start.
http://java.sun.com/docs/books/tutorial/
http://java.sun.com/javaee/5/docs/tutorial/doc/bnadp.html

Porting from PHP to Java - framework recommendations?

Im porting a project from php to java. The project is a web-app based on php and ajax techniques with a javascript front-end. What java-frameworks would you use for something like this?

Does the result have to be written in Java, or does it just have to run on the JVM? In the latter case, you might want to consider Grails, which uses Groovy, a Java-based dynamic language that compiles to Java byte code and has full access to the Java standard API.

How well do you know Java?
Why are you porting it?
I can't really tell based on your description, but there are lots of Java web frameworks out there. Pick one. I prefer Spring.
I fear that you're about to be very disappointed. I anticipate a lot of questions like "Why can't I do X in Java? It's easy in PHP!"

Apache Wicket is a possible java based web framework you might consider. The default would be the java servlet and jsp frameworks.

without seeing the source code - you will need a complete rewrite. just "porting" will probably not work.
out of all available frameworks i'd recommend two: wicket if you want clean lightweight technology. with ajax. jsf/seam if you are in a corporate environment where it it easy to get tons of experienced developers.

I really like Stripes.
There's a really good book out on it too. Stripes ... and Java Web Development is Fun Again.

This question seems to come up alot. Related:
What Web Application Framework for Java is Recommended?
Best java mvc framework implementation for web apps
Does it make sense to use a framework for a simple java web app?
What language/platform to choose for a new web application?

In my opinion you would still do the same but generate the html with JSP and javabeans instead of php. javascripts and ajax will still work without a problem if the outputed html is the same.

It depends by the size of your project, the features and your resources.
If the project have'nt a lot of particular needs you can use Struts. Thsi is a stable framework, not really advanced but simple and powerfull for the development.
Another frameworks more recent and advanced are Spring and Wicket.
Before you start, I recommend you to do a check-list of your need:
Do you must porting a O/R mapping too?
Have you a stable developer knowing Java/J2EE?
Do you think to add some feature during the porting or in short-run?
etc etc
good luck! :)

I would port it to GWT
Google Web Toolkit (GWT) is a development toolkit for building and optimizing complex browser-based applications. Its goal is to enable productive development of high-performance web applications without the developer having to be an expert in browser quirks, XMLHttpRequest, and JavaScript. GWT is used by many products at Google, including Google Wave and the new version of AdWords. It's open source, completely free, and used by thousands of developers around the world.